This study leverages frame-wise speaker counting to switch between speech enhancement and speaker separation for continuous speaker separation. The proposed approach counts the number of speakers at each frame. If there is no speaker overlap, a speech enhancement model is used to suppress noise and reverberation. Otherwise, a speaker separation model based on permutation invariant training is utilized to separate multiple speakers in noisy-reverberant conditions. We stitch the results from the enhancement and separation models based on their predictions in a small augmented window of frames surrounding an overlapped segment. Assuming a fixed array geometry between training and testing, we use multi-microphone complex spectral mapping for enhancement and separation, where deep neural networks are trained to predict the real and imaginary (RI) components of direct sound from stacked reverberant-noisy RI components of multiple microphones. Experimental results on the LibriCSS dataset demonstrate the effectiveness of our approach.